As the clock ticks down to Britain's scheduled exit on March 29, May is trying to persuade the European Union to change a deal that was agreed between London and Brussels late a year ago but overwhelmingly rejected by parliament in January.
Communities Secretary James Brokenshire said Parliament would get to pass judgment on May's Brexit plan "no later than February 27".
The opposition Labour party has denounced May's strategy as time-wasting aimed at forcing parliament to vote through a deal at the last moment.
In an interview with the Sunday Times Mr Starmer described Mrs May's approach as "reckless" and "blinkered" and blamed her "tunnel vision" for the devastating defeat suffered last month when MPs threw out her Brexit deal by a record 230 votes.
The UK Labour Party will seek to force British Prime Minister Theresa May into a second House of Commons showdown on her Brexit deal by the end of the month.
'We know that businesses are leaving the country, we know that businesses are making plans that will damage communities across the country and just this week we had a new chapter in the unfolding nightmare that the trade deals that the United Kingdom businesses enjoy through the European Union will not be ready in time for leaving'.
'We can't allow that to happen, ' Sir Keir said.
On Thursday - Valentine's Day - MPs will consider a motion on Brexit and a series of amendments, likely to include shadow Brexit secretary Sir Keir Starmer's attempt to impose a new deadline for a vote on the deal.
"There needs to be a day when Parliament says that's it, enough is enough".
The UK has signed an agreement with Switzerland ensuring the trading relationship between the two nations will continue after Brexit, the British government said.
"That gives that sense of timetable, clarity, and objective on what we're doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that parliament very firmly has", Brokenshire told the BBC. Switzerland is not a member of the European Union but is part of its single market.
He told the Sophy Ridge on Sunday programme that it would lead to a "very hard border" on the island of Ireland and is contrary to the Good Friday Agreement, the peace deal he helped negotiate which brought an end to The Troubles.
The EU has urged May to grasp Labour's compromise offer rather than press ahead with her preferred option of getting her own divided party onside by renegotiating a clause in the exit agreement relating to the Northern Irish border.
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